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1.
Anti-plane wave motion is induced in a cylindrically orthotropicelastic solid containing a semi-infinite stress-free crack,by a point impulsive body force. First, the static version ofthe problem is solved for the fracture stress z. Here, a globalsolution is obtained and then examined at the crack tip in orderto determine the nature of the spatial singularity. Next, thedynamic problem is treated and it is found that the dominantspatial singularity for z at the crack tip is the same as inthe static case. However, the dynamic part of the stress intensityfactor, T, may introduce a further singularity. Several equivalentexpressions are presented for T, one of which is examined insome detail.  相似文献   

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3.
Tinh Q. Bui  Chuanzeng Zhang 《PAMM》2012,12(1):147-148
The singular edge-based smoothed finite element method (sES-FEM) is developed for stationary dynamic crack analysis in two-dimensional (2D) elastic solids. The paper aims at providing a better understanding of the dynamic fracture behaviors in linear elastic solids by means of the strain smoothing technique. The strains are smoothed and the system stiffness matrix is performed using the strain smoothing over the smoothing domains associated with the element edges. A two-layer singular five-node crack-tip element is employed while the standard implicit time integration scheme is used for solving the discrete sES-FEM equation system. Dynamic stress intensity factors (DSIFs) are extracted using the domain-form of interaction integrals in terms of the smoothing technique. The normalized DSIFs are compared with reference solutions showing a high accuracy of the sES-FEM. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

4.
In this paper we study the asymptotic behavior and the analyticity of the solutions of the one-dimensional porous-elasticity problem with thermal effect. Our main result is to prove the lack of exponential stability in case of the porous-elasticity with thermal effect when viscoelasticity is present. We prove the analyticity of the problem when a porous viscosity is present. We conclude by showing the impossibility of localization in time of the solutions in the isothermal case.  相似文献   

5.
The distinctive features of the loss of stability of elastic solids which undergo phase transitions are investigated for the case of small deformations. The non-uniqueness of the solution of the boundary-value problem for the describing of the thermodynamic equilibrium of a two-phase body is caused by the non-linearity associated with the unknown interface. The solution can be chosen by comparing the potential energies of the body in the two-phase and single phase states and by analysing of the local stability of the two-phase states. A linearized boundary-value problem is formulated which describes infinitesimal small perturbations of an initial two-phase state which is in thermodynamic equilibrium. Analysis of the stability of the two-phase state reduces to an investigation of the bifurcation points and the behaviour of the small solutions of the system of integrodifferential equations in terms of functions describing the perturbations of the interface. The problem of the non-uniqueness and loss of stability of centrisymmetric equilibrium two-phase deformations is investigated as an example. A theorem concerning the number of centrisymmetric solutions is proved. The energy changes accompanying the formation and development of two-phase states and the stability of the solutions obtained are investigated. The concept of topological instability as a bifurcation is introduced, as a result of which the type of geometry of a solution of the boundary-value problem changes and surfaces of separation of the phases actually appear and disappear. Macrodiagrams of the deformational are constructed which demonstrate the effect of deformation softening in the path of a phase transition.  相似文献   

6.
A. Dorfmann 《PAMM》2004,4(1):390-391
In this paper we focus on the mechanical behaviour of filled natural rubber. Filled elastomers under cyclic loading show noticeable differences between the mechanical response under loading and unloading during the first cycles in oscillation tests. We examine the change in material response associated with the Mullins effect and with cavitation, the latter arising from hydrostatic tensile stresses of sufficient magnitude. Then, we focus on constitutive equations using the theory of pseudoelasticity. Specifically, the strain‐energy function depends on a scalar parameter, which provides a means for modifying the form, thereby reflecting stress softening observed during unloading. The dissipation of energy is also accounted for by the use of a dissipation function, which evolves with the deformation history. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

7.
Summary In two-dimensional elasticity stresses at reentrant corners exhibit singular behavior. The stress field is of the form , where (r, ) are polar coordinates centered at the tip of the corner, andf i (; i are smooth functions. For practical use of this series the eigenvalues i (which are generally complex numbers) are required in order of ascending real part. The problem then is to find the roots of a transcendental equation (eigenequation) in the complex plane and arranged in order of ascending real part.A theorem is proved on the number, location and nature of the roots of this equation with the real part in fixed intervals of length . Excellent initial estimates of the real part of the complex roots become available, and so are bounds, within which single real roots exist. This enables the determination of any number of roots in ascending order of real part. The critical angles at which the eigenvalues change nature are also determined. It is shown that for certain cases and for the symmetric mode of deformation, the eigenvalue =1 does not represent a rigid body rotation, therefore it has to be included in the series representation of the stresses. The coefficientsK i can be determined by recently developed extraction techniques, thus allowing complete determination of the elastic field and enabling its correlation with experimental data on brittle fracture, crack initiation, plastic zone estimation etc.Dedicated to Professor Ivo Babuka on the occasion of his 60th birthdayPresented at the Conference: The Impact of Mathematical Analysis on the Solution of Engineering Problems, 17–19 September 1986, University of Maryland, College Park, Maryland, USA  相似文献   

8.
A finite oscillatory shearing motion is shown to be possible, in the absence of body force, in every homogeneous isotropic compressible or incompressible elastic solid. The spatial geometry is the same for all materials and the nature of the time-dependence, for a particular material, is determined by the generalized shear modulus. A motion of this type and a spatially uniform, time-dependent temperature can be supported in thermoelastic solids, without application of body force or volume supply of heat.  相似文献   

9.
In this paper, the problem of wave propagations in one-dimensional (1D) structures is investigated for the first time by using the discrete singular convolution (DSC), a relatively new and promising numerical approach. For simplicity, the non-regularized Lagrange’s delta sequence kernel is adopted in the DSC for most cases. For comparisons, the Regularized Shannon’s delta kernel is also adopted in the DSC for two cases. Methods for applying the free boundary conditions, concentrated loads and concentrated masses are proposed and validated. Detailed formulations and solution procedures are given. Travelling waves in an isotropic aluminum bar and Timoshenko beam are studied. A high degree of accuracy in simulations by the DSC is observed. Numerical results are compared to those obtained from the spectral finite element (SFE) approach, proved a very efficient method in modeling elastic wave propagations. The comparison highlights the efficiency of the DSC in modeling elastic wave propagations. The present research extends the application range of the discrete singular convolution to problems of elastic wave propagations.  相似文献   

10.
This work discusses the role of highly anisotropic interfacial energy for problems involving a material void in a linearly elastic solid. Using the calculus of variations it is shown that important qualitative features of the equilibrium shape of the void may be deduced from smoothness and convexity properties of the interfacial energy.  相似文献   

11.
This work discusses the role of highly anisotropic interfacial energy for problems involving a material void in a linearly elastic solid. Using the calculus of variations it is shown that important qualitative features of the equilibrium shape of the void may be deduced from smoothness and convexity properties of the interfacial energy.  相似文献   

12.
Some relationships, fundamental to the resolution of interfacewave problems, are presented. These equations allow for thederivation of explicit secular equations for problems involvingwaves localized near the plane boundary of anisotropic elastichalf-spaces, such as Rayleigh, Scholte, or Stoneley waves. Theyare obtained rapidly, without recourse to the Stroh formalism.As an application, the problems of Stoneley wave propagationand of interface stability for misaligned predeformed incompressiblehalfspaces are treated. The upper and lower half-spaces aremade of the same material, subject to the same prestress, andare rigidly bonded along a common principal plane. The principalaxes in this plane do not, however, coincide, and the wave propagationis studied in the direction of the bisectrix of the angle betweena principal axis of the upper half-space and a principal axisof the lower half-space.  相似文献   

13.
Summary Transmission and reflexion of plane acoustic waves through a longitudinal shock wave in elastic isotropic solids are investigated. As a result, the amplitude of the transmitted and reflected waves and the jump of the acceleration of the shock are explicitly determined.
Résumé On envisage la transmission et la réflexion d'une onde acoustique plane par une onde de choc longitudinale dans les solides élastiques isotropes. On détermine explicitement l'amplitude des ondes transmises et réflechies et le saut de l'acceleration du choc.
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14.
Lika Svanadze 《PAMM》2008,8(1):10989-10990
In this paper the linear theory of thermomicrostretch elastic solids is considered. The basic properties of wave numbers of the longitudinal and transverse plane waves are established.The existence of eigenfrequencies of the interior homogeneous boundary value problem (BVP) of steady oscillations is studied. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

15.
We present here a non-conventional model for a themoelastic body, based on the Extended Irreversible Thermodynamics, of physical processes in which mass diffusion occurs. Then we linearize the field equations around a constant state in order to obtain the dispersion relation pointing out the interaction between diffusive field and thermal field.  相似文献   

16.
We present here a non-conventional model for a themoelastic body, based on the Extended Irreversible Thermodynamics, of physical processes in which mass diffusion occurs. Then we linearize the field equations around a constant state in order to obtain the dispersion relation pointing out the interaction between diffusive field and thermal field.  相似文献   

17.
A two-dimensional model for stage I short crack propagation on multiple slip planes under the influence of hydrogen is presented. It considers elastic-plastic material behaviour by allowing sliding on the active slip planes in the corresponding slip directions. A crack propagation law based on the crack tip sliding displacement is used to simulate crack growth. The activation of slip bands and the sliding on these active slip bands will be influenced by the local hydrogen concentration. The model is solved numerically using the boundary element method. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

18.
In this paper we investigate the temporal decay behavior of the solutions of the one-dimensional problem in various theories of continua with voids. It has been proved that the coupling of the elastic structure with porous microstructure is weak in the sense that in many situations the temporal decay of solutions is slow. We have considered some theories of porous continua when the deformation-rate tensor or time-rate or porosity function or thermal effects is present. We have proved that the decay cannot be controlled by a negative exponential. The natural question now is whether there exist or not a polynomial rate of decay of the solution in some appropriate norms. In this paper we consider some cases where the decay is slow and we obtain polynomial decay estimates. In concrete we consider the case when only the viscoelastic effect is present, the case when the motion of voids is assumed to be quasi-static and the porous viscosity is present and we finish with the case of the porous-elasticity when thermal effect is coupled.  相似文献   

19.
An accurate method which directly accounts for the interactions between different microcracks is used for analyzing the elastic problem of multiple cracks solids. The effective elastic moduli for randomly oriented cracks and parallel cracks are evaluated for the representative volume element (RVE) with microcracks in infinite media. The numerical results are compared with those from various micromechanics models and experimental data. These results show that the present method is simple and provides a direct and efficient approach to dealing with elastic solids containing multiple cracks. Project supported by the National Natural Science Foundation of China (Grant No. 19704100), and the National Natural Science Foundation of Chinese Academy of Sciences (Project KJ951-1-201).  相似文献   

20.
The decay of solutions in nonsimple elasticity with memory is addressed, analyzing how the decay rate is influenced by the different dissipation mechanisms appearing in the equations. In particular, a first order dissipation is shown to guarantee the asymptotic stability of the related solution semigroup, but is not strong enough to entail exponential stability. The latter occurs for a dissipation mechanism of the second order, that is, the same order as the one of the leading operator.  相似文献   

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